# What does “steep incentive contract” mean in the context of adverse selection?

This term was mentioned in a slide and when I looked online, the only thing which I could find talking about this is this paper.

For example,in the cost-plus-incentive contract

$$x(T, c) = a(T) - a'(T) × (T-c)$$

where $$x$$ is the contractor's fee, $$T$$ is the cost target, $$c$$ is a verifiable cost; $$a(T)$$ is decreasing and convex.

I was told that with smaller $$T$$ and hence higher $$a(T)$$ and $$-a'(T)$$, the incentive contract is steeper. Is the steepness represented by $$-a'(T)$$? What exactly is the interpretation of steepness of incentive contract? Does it mean more risk for the contractor? If this is the case, am I correct that the decreasing $$a(T)$$ motivates the contractor to take a smaller T? How is it translated to incentive constraint? That high-cost contractor would not recklessly take a small T?

In your example, I believe the decreasing nature of $$a(T)$$ is capturing the movement from a low-cost (less risky) project to a high-cost (more risky) project. As the cost (risk) for the project increases, the principal will want a steep incentive scheme to ensure that only a high-skilled contractor will choose to perform the task. This is because we are shifting the weight away from $$a(T)$$ (the fixed payment) and towards $$a'(T) \times (T-C)$$ (the bonus/penalty) as $$T$$ increases. Moving the other direction, as the cost (risk) for the project decreases, $$a(T)$$ increases and the incentives have less power.